Will desitin (zinc oxide diaper cream) (for baby's diaper rash) work on an adult rash?

Open to air. The best remedy for diaper rash is to clean the area thoroughly and often. After cleaning air dry or fan with your hand or use a blow dryer on cool. Leave the diaper off when you can. Creams are basically a barrier and when using take care to dry the area off well before applying. Also some diaper rashes will require medicated cream. You may want to call your pediatrician.
Sometimes. Desitin (zinc oxide diaper cream) is a good moisturizer and skin protection barrier. That's what makes it good for diaper rash. If your adult rash needs a good moisturizer and skin protection barrier, then Desitin (zinc oxide diaper cream) will help. If you have a ringworm or a skin infection, it will help the appearance but not the rash.
Yes. For adult “diaper” rash keep skin clean & dry. Change diaper as soon as it's soiled or wet. For healing go without diaper for periods of time so affected area can air out. Avoid tight diapers or airtight covers over diaper. Meds your Dr. might recommend include antifungal cream (for fungus), a steroid cream (for significant inflammation) or an antibiotic (for bacterial infection.)